2 ieee transactions on mobile computing, …scott f. midkiff, senior member, ieee, and jeffrey h....

Beyond Overlay: Reaping Mutual Benefitsfor Primary and Secondary NetworksThrough Node-Level Cooperation

Xu Yuan,Member, IEEE, Yi Shi, Senior Member, IEEE, Xiaoqi Qin, Student Member, IEEE,

Y. Thomas Hou, Fellow, IEEE, Wenjing Lou, Fellow, IEEE, Sastry Kompella, Senior Member, IEEE,

Scott F. Midkiff, Senior Member, IEEE, and Jeffrey H. Reed, Fellow, IEEE

Abstract—Existing spectrum sharing paradigms have set clear boundaries between the primary and secondary networks. There is

either no or very limited node-level cooperation between the primary and secondary networks. In this paper, we develop a new and bold

spectrum-sharing paradigm beyond the state of the art for future wireless networks. We explore network cooperation as a new

dimension for spectrum sharing between the primary and secondary users. Such network cooperation can be defined as a set of

policies under which different degrees of cooperation are to be achieved. The benefits of this paradigm are numerous, as they allow

integrating resources from two networks. There are many possible node-level cooperation policies that one can employ under this

paradigm. For the purpose of performance study, we consider a specific policy called United cooperation of Primary and Secondary

(UPS) networks. UPS allows a complete cooperation between the primary and secondary networks at the node level to relay each

other’s traffic. As a case study, we consider a problem with the goal of supporting the rate requirement of the primary network traffic

while maximizing the throughput of the secondary sessions. For this problem, we develop an optimization model and formulate a

combinatorial optimization problem. We also develop an approximation solution based on a piece-wise linearization technique.

Simulation results show that UPS offers significantly better throughput performance than that under the interweave paradigm.

Index Terms—Cognitive radio, node-level cooperation, primary network, secondary network, spectrum sharing

Ç

1 INTRODUCTION

THE last decade has witnessed rapid advance in theresearch and development of spectrum-sharing technol-

ogies. Recent report by the President’s Council of Advisorson Science and Technology (PCAST) [16] called for the shar-ing of 1 GHz of federal government radio spectrum withnon-government entities in order to spur economic growth.This report further accelerated the pace of commercializa-tion of innovative spectrum-sharing technologies. As a con-tributor (J.H. Reed) to the PCAST report, our team began torealize that what was needed was a much more aggressiveand broader vision for enhancing spectrum utilization. In[7], Goldsmith et al. outlined three spectrum-sharing para-digms for cognitive radios (CR), namely underlay, overlay,and interweave. These three paradigms were defined froman information theoretic perspective, solely based on howmuch side information (e.g., channel conditions, codebooks)is available to the CRs. In the networking community, thesethree paradigms have been mapped into specific scenariosof how primary and secondary networks interact witheach other for data forwarding. Specifically, the interweave

paradigm refers to the simple idea that secondary users areallowed to use a spectrum band allocated to the primaryusers only when the primary users are not using the band[1], [2], [3], [6], [8], [21], [28]. This paradigm is analogous tothe classic interference avoidance in medium access, or inCR terminology, dynamic spectrum access (DSA). This isthe prevailing scenario on which most of research effortshave been devoted by the CR community in recent years.

The underlay paradigm refers to that secondary users’activities or interference on primary users is negligible (orbelow a given threshold). In contrast to the interweave para-digm, secondary users may be active concurrently with theprimary users in the same vicinity and in the same fre-quency. Potential interference from the secondary usersmay be properly canceled (by the secondary users) via vari-ous interference cancelation (IC) techniques so that residualinterference are negligible to the primary users [5], [13],[24], [25], [27].

Finally, the overlay paradigm requires that the secondaryusers have the primary users’ codebook and messages sothat the secondary users can help maintain or improve thecommunication of the primary users while still achievingsome communication on their own. This is accomplishedthrough sophisticated signal processing and coding (e.g.,dirty paper coding (DPC) [4], [22] and power allocation [12]).From a networking perspective, the overlay paradigm can beinterpreted as having secondary users help forward traffic ofthe primary users on top of its own communications.

Under the interweave and underlay paradigms, the pri-mary and secondary networks are independent (in terms of

� X. Yuan, Y. Shi, X. Qin, Y. T. Hou, W. Lou, S. F. Midkiff, and J. H. Reed arewith the Virginia Polytechnic Institute and State University, Blacksburg,VA 24061. E-mail: {xuy10, yshi, xiaoqi, thou, wjlou, midkiff, reedjh}@vt.edu.

� S. Kompella is with the U.S. Naval Research Laboratory, Washington, DC20375. E-mail: [email protected].

Manuscript received 19 Nov. 2014; revised 16 Dec. 2015; accepted 2 Mar.2016. Date of publication 7 Mar. 2016; date of current version 1 Dec. 2016.For information on obtaining reprints of this article, please send e-mail to:[email protected], and reference the Digital Object Identifier below.Digital Object Identifier no. 10.1109/TMC.2016.2539161

2 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 16, NO. 1, JANUARY 2017

1536-1233� 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

data forwarding in each network). On the other hand, underthe overlay paradigm, there is some level of cooperation bythe secondary network. Inspired by this primitive coopera-tion idea in the overlay paradigm, there have been somerecent efforts [9], [10], [14], [15], [19], [20], [26] on how toexploit possible cooperation from secondary users for thebenefit of data forwarding. We will review these efforts indetail in Section 2. To summarize, the focus of these effortshas been limited to having secondary nodes help relay pri-mary nodes’ traffic. This, as we envision in this paper, isonly a tip of the iceberg.

In this paper, we develop a paradigmwith amuch broadervision beyond the state of the art. We explore network coopera-tion as a new dimension for spectrum sharing between pri-mary and secondary nodes. Such network cooperation can bedefined as a set of policies under which different degrees ofcooperation are to be achieved. Corresponding to each coop-eration policy, a traffic-forwarding behavior for primary andsecondary users can be defined. One such primitive policy, asthat in [9], [10], [14], [15], [19], [20], [26], is to have secondarynetwork help relay primary users’ traffic. Another policy(United cooperation of Primary and Secondary (UPS) [23]),which we will use as a main policy example in this paper, isto allow complete node-level cooperation between theprimary and secondary networks for data forwarding. Thesetwo examples are amongmany possible policies that one candefine to achieve network sharing between primary andsecondary networks.

To concretize our discussion on policy-based networksharing, we consider the UPS policy in detail, where UPS isthe abbreviation of United cooperation of Primary and Sec-ondary networks [23]. UPS represents a policy that allows acomplete cooperation between the primary and secondarynetworks to relay each other’s traffic. For performance eval-uation, we study a problem with the goal of supporting therate requirements of the primary sessions while maximizingthe throughput of the secondary sessions. A number of tech-nical challenges must be addressed in this problem, includ-ing how to provide guaranteed service for the primarytraffic while supporting as much the secondary traffic aspossible, how to select the optimal relays and routing pathsfor each source and destination pair, and how to coordinatethe transmission and interference relationship between theprimary and secondary nodes. For this problem, wedevelop an optimization model and formulate a combinato-rial optimization problem. Although the problem is in theform of mixed-integer nonlinear program (MINLP), wedevelop an approximation solution based on the piece-wiselinearization technique that allows to transform this prob-lem into a mixed-integer linear program (MILP). Throughsimulation results, we demonstrate that UPS policy offerssignificantly better throughput performance than that underthe existing interweave paradigm.

The remainder of this paper is organized as follows. InSection 2, we review related work on primary and second-ary network cooperation. In Section 3, we outline our visionof policy-based network cooperation and use UPS as anexample. In Section 4, we use UPS as a case study for perfor-mance evaluation. For UPS, we develop an optimizationmodel and formulate an optimization problem. In Section 5,we propose an approximation solution for the UPS

throughput optimization problem. Section 6 presents simu-lation results to demonstrate the benefits and advantages ofthe UPS policy. Section 7 concludes this paper and pointsout future research directions.

2 RELATED WORK

Due to space limitation, we will focus our attention on recentresearch efforts related to primary and secondary networkcooperation. We find that all these efforts only consideredhaving the secondary network help relay traffic for the pri-mary network. In [19], Simeone et al. proposed to have theprimary network lease its spectrum in the time domain tothe secondary network in exchange for having the secondarynetwork relay its data. In [26], Zhang and Zhang formulatedthis model as a Stackelberg game and a uniqueNash Equilib-rium point was achieved for maximizing primary and sec-ondary users’ utilities in terms of their transmission ratesand revenue. In [20], Su et al. proposed to have the primarynetwork lease its spectrum in the frequency domain to thesecondary network to relay its data in order to maximize pri-mary users’ energy saving and secondary users’ data rates.In [10], Jayaweera et al. proposed a new way to encourageprimary users to lease their spectrum by having secondaryusers place bids on the amount of power they are willing toexpend for relaying primary users’ traffic. In [9], Hua et al.proposed a MIMO-based cooperative CR network where thesecondary users utilize MIMO’s antenna diversity to helprelay primary users’ traffic while transmitting their own traf-fic. In [14], Manna et al. considered the three-node model in[11]. The relay node was assumed to be a secondary nodeand have MIMO capability. The primary transmitter leasesthe second time slot to the secondary node (relay node) sothat the secondary node can use the time slot to help relaythe primary node’s traffic while transmitting its own data. In[15], Nadkar et al. considered how to offer incentive (in termsof time and frequency) to a secondary network to help trans-mit primary user traffic. They studied a cross-layer optimiza-tion problem that maximizes transmission opportunities forsecondary users while offering a guaranteed throughput tothe primary users.

In all these efforts involving node-level cooperationbetween the primary and secondary networks, the focushas been limited to having secondary nodes help primarynodes in relaying primary users’ traffic. As discussed, thisis only a tip of the iceberg on network cooperation. In thispaper, we envision much broader cooperation between thetwo networks.

3 CASE OF POLICY-BASED NETWORK

COOPERATION

As discussed in Section 1, the goal of this paper is to outlinea broad vision of policy-based network cooperationbetween the primary and secondary networks as a newdimension in radio spectrum sharing. Here, a policy definesthe scope of cooperation at the node-level between the twonetworks. Such cooperation policies could vary from unilat-eral cooperation (i.e., only secondary nodes help relay pri-mary user traffic but not vice versa), bilateral cooperation,constrained cooperation, or other customized policy basedon particular application needs or requirements.

YUAN ETAL.: BEYOND OVERLAY: REAPING MUTUAL BENEFITS FOR PRIMARYAND SECONDARY NETWORKS THROUGH NODE-LEVEL... 3

As a concrete example, we consider the UPS policy dis-cussed in Section 1, which represents an interesting andextreme scenario where there is complete cooperationbetween the primary and secondary networks. Fig. 1 illus-trates the UPS policy for multi-hop primary and secondarynetworks. Unlike overlay, which is limited to only allowingsecondary nodes help relay primary nodes’ traffic, UPSallows primary nodes to help relay secondary nodes’ trafficas well. From a network resource perspective, the UPS policyallows the pooling of all the resources from primary and sec-ondary networks together and allows users in each networkto access much richer network resources in a combined net-work. Note that although the two networks are combinedinto one at the physical level, priority or service guarantee tothe primary network traffic can still be enforced by imple-menting appropriate traffic engineering rules.

It is not hard to see that there are many potential benefitsassociated with the UPS policy. We briefly describe thesebenefits as follows:

� Topology. Comparing to having primary and second-ary nodes being independent for each other, thecombined network allows both primary and second-ary networks a much improved connectivity withnodes from both networks.

� Power Control. As more nodes fall in the maximumtransmission range of a primary or secondary node,this node has more flexibility in choosing its nexthop node via power control. This flexibility can beexploited for different upper layer performancerequirements or objectives.

� Link Layer. The improved physical topology allowsmore opportunities at the link layer for spectrumaccess. Both the primary and secondary networkscan better coordinate with each other in transmissionand interference avoidance. Further, the potentialissue associated with link failure can now be miti-gated effectively.

� Network Diversity. The combined network offersmore routing opportunities to users in both net-works. This directly translates into improvedthroughput and delay performance for user sessions.

� Service and Applications. The UPS architecture (com-bining both primary and secondary networks)allows to offer much richer services and applicationsthan those services that were studied in [9], [10],[14], [15], [19], [20], [26]. Although the two networks

are combined, the services and applications offeredto users in each network can still be supported, byimplementing certain traffic engineering policies. Inother words, the combined network does not meanthat service guarantee to the primary network willbe lost. On the contrary, by specifying the desiredresource management policy appropriately in thecombined network, one can easily achieve variousservice differentiation objectives and applicationgoals, as we shall describe in a case study in the restof this paper.

The above UPS only represents one policy under the pol-icy-based network cooperation paradigm. There are manyother policies that can also be considered, ranging from nocooperation, unilateral cooperation, constrained coopera-tion, among others. Interweave and UPS can be consideredtwo extreme cases of the policy space for network coopera-tion. The overlay paradigm that we discussed earlier (i.e.,only secondary nodes helping primary traffic but not viceversa) may resemble the unilateral sharing policy, whichcan be viewed as a policy between the interweave and UPS.The constrained cooperation policy allows each network toonly engage a subset of its nodes in network cooperation.The motivation of this policy is that certain nodes in eithernetwork may be too critical or sensitive (e.g., due to securityconcerns) in its own network and are thus prohibited frominteracting with nodes from the other network. This con-strained cooperation may be viewed as a generalization ofinterweave and UPS. Again, the policies discussed aboveonly represent a few among a lot of possibilities. The defini-tion of a policy is up to the network operators and it deter-mines the scope of cooperation between the two networks.

The policy-based node-level cooperation paradigm mayoffer many possibilities and potential benefits for both theprimary and secondary networks. From a networking per-spective, the improved network connectivity, increased flex-ibility in power control, scheduling and routing all translateinto improved forwarding performance for primary andsecondary users’ traffic. From a spectrum-sharing perspec-tive, the ability to access other network infrastructure helpsimprove spatial diversity, thus allowing users to tap unusedspectrum in the spatial domain. From economic perspec-tive, such shared network infrastructure reduces the cost ofinfrastructure needed for each individual network (byallowing the tapping of another network’s infrastructureresource), thus helping to enable traditionally underservedpopulation and areas to benefit from current and future

Fig. 1. Network topologies under the interweave and the UPS policy.


wireless-enabled goods and services. But from regulatoryperspective, the proposed policy-based node-level coopera-tion paradigm may be ahead of its time. But there is no rea-son why we should not investigate its capability andrecognize its potential from a research perspective. This isthe goal of this paper.

4 CASE STUDY: UPS POLICY

4.1 Problem Scope

In the rest of this paper, we offer an in-depth study of theUPS policy. Referring to Fig. 1, suppose that there is a set ofsessions in the primary network, with each session having acertain rate requirement. In the secondary network, supposethere is also a set of sessions, with each session having anelastic traffic requirement. By “elastic”, we mean that eachsecondary session does not have a stringent rate require-ment as the primary session. Instead, each secondary ses-sion will be supported on a best-effort basis and willtransmit as much as the remaining network resource allows.A plausible goal under the UPS policy could be to have thecombined network to support the rate requirements of theprimary sessions while maximizing the throughput of thesecondary sessions.

For this problem, there are a number of technical chal-lenges that one must address:

• Guaranteed service for primary traffic. Since each pri-mary session is assumed to have a hard rate require-ment, the combined network should support it at allpossibility. This problem alone may not be challeng-ing. What is challenging (and interesting) is thatshould there are multiple ways to support primarysessions’ rate requirements. We should find such away that the rates for the secondary sessions aremaximized in the combined network.

• Relay selection. To meet the service requirement(guaranteed service for primary traffic) and to opti-mize the objective (maximize the rates of secondarysessions), relay node selection along a route (foreither a primary or secondary session) is not a trivialproblem.

• Scheduling. To maximize the rates of the secondarysessions while guaranteeing the rates of the primarysessions, scheduling in each time slot needs to becarefully designed. In particular, in addition toaddressing traditional self-interference (half-duplex)and mutual-interference problems, the primary net-work must be cooperative so as to help the second-ary sessions to achieve their optimization objectivein the combined network. Such cooperative behaviorfrom the primary network is a key in the UPS policyand has not been explored in prior efforts.

4.2 Mathematical Modeling

In this section, we develop a mathematical model for theUPS policy. Table 1 lists notation in this paper. Denote N asthe combined set of nodes consisting the set of primary

nodes N P and the set of secondary nodes N S, i.e.,

N ¼ N P

SN S. In the combined network, denote T i as the

set of nodes (including both primary and secondary nodes)

that is located within a nodes i’s transmission range, wherei can be either a primary or secondary node (i.e., i 2 N ).Denote J i as the set of nodes (including both primary andsecondary nodes) that is located within node j’s interferencerange, where j can be either a primary or secondary node.

For a primary session l 2 L, we assume it has a hard

requirement on its data rate, which we denote as RðlÞ. For asecondary session m 2 L, we assume that it does not have arate requirement. Instead, the data rate rðmÞ on m 2 L issupported on a best-effort basis and will be an optimizationvariable in the problem formulation.

Guaranteed service for the primary sessions. For primarysessions, they consider the combined network N as theircommunication resources. For flexibility and load balancing,we allow flow splitting in the network. That is, the flow rateof a session may split and merge inside the network in what-ever loop-free manner as long as it can help support the

given rate requirement RðlÞ of session l 2 L. Denote fijðlÞ asthe data rate on link ði; jÞ that is attributed to primary session

l 2 L, where i 2 N and j 2 T i. Denote sðlÞ and dðlÞ as the

source and destination nodes of primary session l 2 L,respectively.We have the following flow balance constraints:

• If node i is the source node of primary session l 2 L(i.e., i ¼ sðlÞ), then

Xj2T i

fijðlÞ ¼ RðlÞ ðl 2 LÞ: (1)

• If node i is an intermediate relay node for primary

session l (i.e., i 6¼ sðlÞ and i 6¼ dðlÞ), then

TABLE 1Notation

Primary Network

N P The set of primary nodesL The set of primary sessionsfijðlÞ The flow rate traversing on link ði; jÞ that is attributed to

primary session l 2 L; i; j 2 NsðlÞ The source node of primary session l 2 LdðlÞ The destination node of primary session l 2 LRðlÞ The data rate requirement of primary session l 2 L

Secondary NetworkN S The set of secondary nodesL The set of secondary sessionsfijðmÞ The flow rate traversing on link ði; jÞ that is attributed to

secondary sessionm 2 L; i; j 2 NsðmÞ The source node of secondary sessionm 2 LdðmÞ The destination node of secondary sessionm 2 LrðmÞ The data rate achieved by secondary sessionm 2 L

Combined Network

N The set of all nodes in the network,N ¼ N P

SN S

Cij The link capacity of link ði; jÞ; i; j 2 Nxij½t� ¼ 1 if node i is transmitting data to node j in time slot t,

and is 0 otherwiseT i The set of nodes that are located within the transmission

range of node i 2 NJ i The set of nodes that are located within the interference

range of node i 2 NT The number of time slots in a frame


Xj6¼sðlÞ

j2T i

fijðlÞ ¼Xk6¼dðlÞ

k2T i

fkiðlÞ ðl 2 L; i 2 N PÞ: (2)

• If node i is the destination node of primary session l

(i.e., i ¼ dðlÞ), thenXk2T i

fkiðlÞ ¼ RðlÞ ðl 2 LÞ: (3)

It can be easily verified that once (1) and (2) are satisfied,then (3) is also satisfied. As a result, it is sufficient to listonly (1) and (2) in the formulation.

Best-effort service for secondary sessions. Under theUPS policy, the primary sessions have priority in accessthe combined network resources (in the form of guaran-teed services). Once the primary sessions are supported,the secondary sessions may use as much as the remainingresources in the combined network. How the primary andsecondary sessions interact in the combined networkshould be part of an optimization problem. Denote fijðmÞas the data rate on link ði; jÞ that is attributed to secondarysession m 2 L. Denote sðmÞ and dðmÞ as the source anddestination nodes of secondary session m 2 L, respectively.Similar to that for the primary sessions, we allow flowsplitting for the secondary sessions. We have the followingflow balance constraints:

• If node i is the source node of secondary sessionm 2 L (i.e., i ¼ sðmÞ), then we have

Xj2T i

fijðmÞ ¼ rðmÞ ðm 2 LÞ: (4)

• If node i is an intermediate relay node for secondarysessionm (i.e., i 6¼ sðmÞ and i 6¼ dðmÞ), then

Xj 6¼sðmÞ

j2T i

fijðmÞ ¼Xk6¼dðmÞ

k2T i

fkiðmÞ ðm 2 L; i 2 N SÞ: (5)

• If node i is the destination node of secondary sessionm (i.e., i ¼ dðmÞ), then

Xk2T i

fkiðmÞ ¼ rðmÞ ðm 2 LÞ: (6)

Again, to avoid redundancy, it is sufficient to list only (4)and (5) in the formulation.

Note that although (4)-(6) are similar to (1)-(3), there is animportant difference between them: unlike RðlÞ for primary

session l 2 L, which is a given constant, secondary sessionrate rðmÞ, m 2 L, is an optimization variable. Therefore, forthe primary sessions, we only need to optimize their flowpaths, while for the secondary sessions, we need to optimizeboth their routes and their rates.

Self-interference constraints. We assume scheduling isdone in time slot on a frame-by-frame basis, with eachframe consisting of T time slots. We use a binary variablexij½t�; i; j 2 N and 1 � t � T , to indicate whether node i

transmits data to node j. That is,

xij½t� ¼1 If node i transmits data to node j

in time slot t;0 otherwise;

8<:

where i 2 N ; j 2 T i, and 1 � t � T .Assuming each primary or secondary session is unicast,

a node i only needs to transmit to or receive from one nodein a time slot. We have

Xj2T i

xij½t� � 1 ði 2 N ; 1 � t � T Þ ; (7)

Xk2T i

xki½t� � 1 ði 2 N ; 1 � t � T Þ : (8)

To account for half-duplex at each node i, we have:

xij½t� þ xki½t� � 1 ði 2 N ; j; k 2 T i; 1 � t � T Þ : (9)

These three constraints in (7), (8) and (9) can be replacedby the following single constraint,

Xj2T i

xij½t� þXk2T i

xki½t� � 1 ði 2 N ; 1 � t � T Þ: (10)

To see this, note that in (10), if node i is receiving data fromsome node in T i in time slot t, we must haveP

j2T ixij½t� ¼ 0, i.e., node i cannot transmit in the same time

slot. This is exactly the half-duplex constraint. In this case,(10) also becomes (8). On the other hand, if node i is trans-mitting to some node in T i in time slot t, thenP

k2T ixki½t� ¼ 0, i.e., node i cannot receive in the same time

slot. Again, this is the half-duplex constraint. In this case,(10) becomes (7).

Mutual interference constraints. To model mutual inter-ference constraints, we assume that for any primary or sec-ondary node j 2 N that is receiving data in time slot t, itshall not be interfered by another (unintended) transmittingnode p 2 I j in the same time slot. We have the followingmutual interference constraint:

xij½t� þ xpk½t� � 1 ; (11)

where i 2 T j; p 2 J j; k 2 T p; j 2 N ; j 6¼ k; and 1 � t � T .Following the same token in (10), the three constraints in

(7), (8) and (11) can be replaced by the following single andequivalent constraint,

Xi2T j

xij½t� þXk2T p

xpk½t� � 1 ; (12)

where p 2 J j; j 2 N ; j 6¼ k; and 1 � t � T .Link rate constraints. For each link ði; jÞ, denote the link

capacity as Cij, e.g., Cij ¼ B log 2ð1þQid

�aij

�

N0Þ, where B is

bandwidth, Qi is the power spectral density from transmitnode i, dij is the distance between node i and j, a is the pathloss index, � is the antenna related constant, and N0 is theambient Gaussian power spectral density. Since the aggre-gate flow rate from the primary and secondary sessions oneach link ði; jÞ cannot exceed the average link rate (over T


time slots), we have

Xj6¼sðlÞ;i6¼dðlÞ

l2L

fijðlÞ þXj 6¼sðmÞ;i6¼dðmÞ

m2LfijðmÞ � 1

T

XTt¼1

Cij � xij½t�: (13)

4.3 Problem Formulation

In the combined network, our goal is to offer guaranteedsupport for the primary sessions (each with a given raterequirement) while maximizing the throughput for the sec-ondary sessions, whose traffic is assumed to be elastic. Formaximizing secondary network throughput, different objec-tive functions can be explored to satisfy network require-ment. In [23], we considered a simple case with linearobjective function (i.e., maximizing the minimum through-put). In this paper, we will consider a nonlinear objectivefunction. We use a utility function ln rðmÞ for m 2 L as ourobjective. Such utility function is widely used in the litera-ture [17]. We have the following problem formulation:

OPTmax

Pm2L ln rðmÞ

s.t. Guaranteed service for primary sessions: (1), (2);Best effort service for secondary sessions: (4), (5);Self interference constraints: (10);Mutual interference constraints: (12);Link capacity constraints: (13).

In this formulation, RðlÞ and Cij are constants, xij½t� arebinary variables, fijðlÞ; fijðmÞ and rðmÞ are continuous vari-ables. Due to nonlinear terms ln rðmÞ in the objective func-tion and binary variables xij½t�, the optimization problem isa mixed-integer nonlinear programming, which is NP-hard ingeneral. In the next section, we develop an approximationalgorithm to solve this problem.

5 AN APPROXIMATE SOLUTION

5.1 Overview

In this section, we develop an approximate solution to OPTwith guaranteed performance. For the nonlinear log term in

the objective function of OPT, one could relax the nonlinearfunction with a series of linear functions. The issue here ishow to achieve such linearization with performance guaran-tee. This is the focus of our proposed solution.

For a target performance gap � between the optimalobjective (unknown) and the approximate objective (thatwe aim to develop), we will develop an algorithm to deter-mine a set of piece-wise linear segments that approximatethe log function (See Fig. 2). The essence of our linearapproximation is to find just the right number of linear andunequal-length segments to approximate the log function.The idea is that, for a given performance gap �, we can cal-culate the maximum linear approximation error, say h, thatis allowed in the linearization. Then, we can develop analgorithm (Section 5.2) to find the slopes and starting pointsfor the set of linear segments. Subsequently, the nonlinearlog terms in OPT can be replaced by a set of linear con-straints and we have a new linearized optimization prob-lem, which we denote as OPT-L. Although OPT-L is in theform of mixed-integer linear programming, the integer varia-bles are all binary. We find that commercial software (suchas CPLEX) can solve such binary MILP efficiently.

5.2 Linearization

Our goal of linear approximation of ln rðmÞ is to replaceln rðmÞ with the minimum number of linear segments whileensuring that the difference between any point on ln rðmÞand its corresponding linear segment is no more than h.Denote Km as the minimum number of line segments suchthat each segment meets the error requirement (i.e., h).Denote rLðmÞ and rUðmÞ as the lower and upper bounds forrðmÞ, respectively. For rLðmÞ, we can set it to an arbitrarilysmall positive value. For rUðmÞ, we can set it to maxi;j2NCij,

the maximum capacity among all links. Denoter0ðmÞ; r1ðmÞ; . . . ; rKmðmÞ as values on the X-axis for the endpoints of these Km segments, with r0ðmÞ ¼ rLðmÞ andrKmðmÞ ¼ rUðmÞ.

The minimum number of line segments Km can be foundwith the following iterative process. We start from r0ðmÞ tocalculate the slope of the first segment, which must ensurethat this segment satisfies the error bound h. After finding thisslope,we can find the right-side end point of the first segment.From this point, we repeat the same process for the secondsegment and so forth, until the last segment exceeds rUðmÞ.

Specifically, denote slope of the kth linear segment asqkðmÞ, i.e.,

qkðmÞ ¼ ln rkðmÞ � ln rk�1ðmÞrkðmÞ � rk�1ðmÞ : (14)

Denote ykðrðmÞÞ as the kth linear segment that approxi-mates ln rðmÞ. Then we have:

ykðrðmÞÞ ¼ qkðmÞ � rðmÞ � rk�1ðmÞ½ � þ ln rk�1ðmÞ; (15)

for rk�1ðmÞ � rðmÞ � rkðmÞ.Referring to Fig. 3, for any point rðmÞ within

rk�1ðmÞ � rðmÞ � rkðmÞ, it is easy to see that the point onthe tangential line (in parallel to the linear segment approxi-mation) that intersects the log curve has the maximumapproximation error h. Denote the X-coordinate of this point

Fig. 2. Piece-wise approximation with line segments.


as r�kðmÞ, we have h ¼ ln r�kðmÞ � ykðr�kðmÞÞ. Since the slope

of tangential line (achieving h) for ln rðmÞ is 1rðmÞ, then

qkðmÞ ¼ 1r�kðmÞ, or r�kðmÞ ¼ 1

qkðmÞ, where qkðmÞ is the slope of

the linear segment ykðrðmÞÞ. Then, we have

h ¼ ln r�kðmÞ � ykðr�kðmÞÞ

¼ ln r�kðmÞ � qkðmÞ � r�kðmÞ � rk�1ðmÞ� �

þ ln rk�1ðmÞh i

¼ ln1

qkðmÞ � qkðmÞ � 1

qkðmÞ � rk�1ðmÞ� �

� ln rk�1ðmÞ

¼ � ln qkðmÞ � 1þ qkðmÞ � rk�1ðmÞ � ln rk�1ðmÞ:

Therefore, we have the following equation:

� ln qkðmÞ þ qkðmÞ � rk�1ðmÞ � ln rk�1ðmÞ þ hþ 1½ � ¼ 0:

(16)

For a give error bound h, the values of r1ðmÞ; . . . ; rKmðmÞand slopes q1ðmÞ; q2ðmÞ; . . . ; qKmðmÞ can be found iterativelythrough the following algorithm:

Algorithm 1. (Piece-wise linearization)Initialization: k :¼ 0 and rkðmÞ :¼ rLðmÞ.While (rkðmÞ < rUðmÞ) {k :¼ kþ 1.Find slope qkðmÞ by solving the equation (16).With qkðmÞ, compute rkðmÞ via (14). }

Km :¼ k; rKmðmÞ :¼ rUðmÞ.Recalculate qKmðmÞwith (14).

The values of qkðmÞ in (16) and rkðmÞ in (14) can besolved by numerical methods such as bisection method orNewton’s method [18].

Lemma 1. The maximum approximation error within each linearsegment as defined by Algorithm 1 is no more than h.

Proof. The proof is based on the above construction. Weomit its discussion here to conserve space. tu

5.3 Approximation Gap

Byusing the piece-wise linearization algorithm (Algorithm 1),we can approximate the log term ln rðmÞwith a series of linearsegments, each with an approximation error no more than h.For rðmÞ, denote yðmÞ as the concatenation of the piece-wiselinear segments constructed by Algorithm 1. Then the objec-tive functionmax

Pm2L ln rðmÞ in OPT is replaced by the fol-

lowing linear objective and a set of linear constraints(representing the convex hull below the linear segments):

maxXm2L

yðmÞ (17)

s:t: yðmÞ � qkðmÞ � ðrðmÞ � rk�1ðmÞÞ þ ln rk�1ðmÞðk ¼ 1; 2; . . . ; Km;m 2 LÞ:

(18)

The original OPT can be re-formulated into a new optimiza-tion problem, which we denote as OPT-L.

OPT-Lmax

Pm2L yðmÞ

s.t. Constraints (1), (2), (4), (5), (10), (12), (13), (18),rLðmÞ � rðmÞ � rUðmÞ, ðm 2 LÞxij½t� 2 f0; 1g; fijðmÞ � 0; fijðlÞ � 0.ði 2 N ; j 2 T i;m 2 L; l 2 L; 1 � t � T Þ,

where xij½t� are binary variables, fijðlÞ; fijðmÞ; rðmÞ and yðmÞare continuous variables, and qkðmÞ; rk�1ðmÞ and RðlÞ areconstants. OPT-L is in the form of mixed integer linear pro-gramming. Since all integers are binary, the MILP problemtends to be solved efficiently by a commercial solver(CPLEX). Our simulation results in Section 6 confirm thatthis is indeed the case.

We now quantify the gap between the optimal objectivevalues of OPT-L and OPT.

Lemma 2. The gap between the optimal objective values of OPTand OPT-L, �, is upper bounded by jLj � h.

Proof. Suppose an optimal solution of OPT is ’�OPT ¼½x�

ij½t�; r�ðmÞ; f�ijðmÞ; f�

ijðlÞ�, with the objective value being

Y �OPT ¼

Pm2L ln r

�ðmÞ. We can construct a feasible solu-

tion to OPT-L, denoted as ’OPT�L, based on ’�OPT as

follows: ’OPT�L ¼ ½xij½t�; rðmÞ; fijðmÞ; fijðlÞ; yðmÞ�, where

xij½t� ¼ x�ij½t�; rðmÞ ¼ r�ðmÞ; fijðmÞ ¼ f�

ijðmÞ and fijðlÞ ¼f�ijðlÞ. Then, ’OPT�L satisfy constraints (1), (2), (4), (5), (10),

(12), (13) in OPT-L. yðmÞ can be calculated by solvingOPT-L with the variables being set to those values in’OPT�L. Suppose that r�ðmÞ falls in the interval½rk�1ðmÞ; rkðmÞ�. Then the objective function

Pm2L yðmÞ

is maximized only when yðmÞ ¼ ykðr�ðmÞÞ ¼ qkðmÞ �ðr�ðmÞ � rk�1ðmÞÞ þ ln rk�1ðmÞ in (18). Denote this objec-tive value in OPT-L as YOPT�L. Then,

Y �OPT � YOPT�L ¼

Xm2L

ln r�ðmÞ �Xm2L

yðmÞ

¼Xm2L

ln r�ðmÞ �Xm2L

ykðr�ðmÞÞ

¼Xm2L

�ln r�ðmÞ � ykðr�ðmÞÞ

�

� jLj � h;

Fig. 3. An illustration of the maximum approximation error for piece-wiseline segment.


where last inequality holds by Lemma 1. We let� ¼ jLj � h.

Now denote ’�OPT�L as an optimal solution for OPT-L,

with the objective value of Y �OPT�L. Since YOPT�L is merely

the objective value of a feasible solution, we haveY �OPT�L � YOPT�L. Then Y �

OPT � Y �OPT�L � Y �

OPT � YOPT�L � �.

This completes the proof. tu

Our complete solution for solving OPT can be summa-rized as follows: For any a given performance gap �, we cancompute linear approximation error h ¼ �

jLj. Based on the

approximation error h, we perform piece-wise linearapproximation through Algorithm 1. Then we reformulateOPT to OPT-L, and solve it by CPLEX.

6 SIMULATION RESULTS

In this section, we present numerical results to demonstratethe capabilities and advantages of the UPS policy. The goalof this section is twofold. First, we show that the UPS policyoffers much better performance for both the primary andsecondary networks than that under the interweave para-digm. Second, we shall have a close look at how the primaryand secondary nodes help each other in the UPS policy.

6.1 Simulation Setting

We consider a UPS network where both the primary and thesecondary nodes are randomly deployed in a 100 100area. For generality, we normalize the units for distance,bandwidth, power and data rate with appropriate dimen-sions. We assume the bandwidth of the channel allocated tothe primary network is B ¼ 10. The number of time slots ina frame is T ¼ 10. The transmission power spectral densityQi for each node i 2 N is 1, the path loss index is 4, theantenna related constant � is 1, and the ambient Gaussian

power spectral density N0 ¼ 10�6. We assume the transmis-sion range and interference range at all nodes are 30 and 50,respectively.

We set the maximum acceptable performance gapbetween the objective of OPT and its linear approximationOPT-L as � ¼ 0:02.

6.2 An Example

We consider a 30-node network, with 15 primary nodes and15 secondary nodes randomly deployed in a 100 100 area(see Fig. 4). The location of each node is given in Table 2. Inthis example, we assume that there are two primary ses-sions in the primary network and two secondary sessions inthe secondary network. The source and destination nodesfor each session are randomly chosen in each network andare shown in Table 3. Denote the rate requirements of the

two primary sessions as Rð1Þ and Rð2Þ, respectively. We

gradually increase the rate requirements of Rð1Þ and Rð2Þand examine (i) whether such rates can be supported underthe UPS policy and the interweave paradigm, respectively,and (ii) the objective values of secondary session utilitiesunder both the UPS policy and the interweave paradigm.

Fig. 4. Region 1 example that showing the flow routing topologies and

scheduling for the primary and secondary sessions, where the solid line

segments are for the primary sessions while the dashed line segments

are for the secondary sessions.

TABLE 2Location of Primary and Secondary Nodes for the

30-Node Network

Primary Node Location Secondary Node Location

P1 (2.5, 85.2 ) S1 (29.6, 76.6)P2 (29.2, 95.5 ) S2 (55.5, 62 )P3 (11.4, 59.1 ) S3 (50.4, 97.1)P4 (45.9, 79) S4 (70.7, 62.2)P5 (63.8, 67.8) S5 (19.1, 87.4 )P6 (54, 41.2) S6 (62, 38.4)P7 (86.3, 56.5) S7 (77, 26.2)P8 (68.4, 87.5) S8 (43.4, 40.8 )P9 (34, 56.3) S9 (92.4, 44.1)P10 (78.3, 41.7) S10 (70.7, 6.6))P11 (33.5, 19.6 ) S11 (20.1, 46.1)P12 (79, 83.7) S12 (92.3, 74.8 )P13 (95.9, 31.5) S13 (88, 96.4)P14 (19.5, 30.1) S14 (2.4, 29)P15 (54.4, 13.8) S15 (92.6, 8.6)


The utility maximization problem for the secondary ses-sions under the interweave paradigm can be formulated fol-lowing a similar token to OPT.

Table 4 shows the approximation gap between the utilityobjective of the linearized problem and the utility objectiveof the original problem under different Rð1Þ and Rð2Þ. Thefirst column represents increasing rate requirements for theprimary sessions. The second column shows the utilityobjectives of the two secondary sessions (abbreviated as“SS” in the table) from the linearized problem OPT-L, whilethe third column shows the utility objectives of the two sec-ondary sessions from the original problem. The fourth col-umn shows the gap between the utility objectives from thelinearized problem and the original problem. Given the tar-get approximation error " ¼ 0:02, all actual approximationerrors fall below this target.

Table 5 summarizes the results of this study. The secondcolumn represents increasing rate requirements for the pri-mary sessions (i.e., Rð1Þ ¼ Rð2Þ). For ease of explanation,we break this table into five regions, with each region repre-senting a specific behavior for comparison between the UPSpolicy and interweave paradigm. The third and fourth

columns show the performance under the UPS policy. Spe-cifically, the third column shows whether the rate require-ments of the two primary sessions can be supported(“feasible”) in the primary network (abbreviated as “PN” inthe table); the fourth column shows the rate utility objectiveof the two secondary sessions (abbreviated as “SS” in thetable) with �1 indicating zero rates for the secondary ses-sions (due to the log function) and “N/A” indicating notapplicable as the corresponding network cannot even sup-port the rate requirements of the primary sessions. The fifthand sixth columns show the performance under the inter-weave paradigm, which are to be compared to the third andfourth columns under the UPS policy, respectively.

Region 1. This region represents the scenario where therate requirements of the primary sessions can be supportedunder both the UPS policy and the interweave paradigm,and the rates of the secondary sessions are positive.

TABLE 3Source and Destination Nodes for Each Session

in the 30-Node Network

Session Source Destination

Primary session 1 P13 P11

Primary session 2 P3 P8

Secondary session 1 S13 S6

Secondary session 2 S14 S2

TABLE 4Approximation Gap Between the SS Utility Objectives

of Linearized Problem and Original Problem

Rate RequirementRð1Þ; Rð2Þ

SS Utility ofLinearized Problem

SS Utility ofOriginal Problem Gap

0 3.7012 3.7128 0.00160.2 3.288 3.3046 0.00160.4 3.288 3.3046 0.00160.6 3.288 3.3046 0.00160.8 3.288 3.3046 0.00161.0 3.288 3.3046 0.00161.2 3.288 3.3046 0.00161.4 3.288 3.3046 0.00161.6 3.288 3.3046 0.00161.8 3.158 3.167 0.00092.0 3.158 3.167 0.00092.2 3.158 3.167 0.00092.4 3.158 3.167 0.00092.6 2.892 2.899 0.0072.8 2.653 2.656 0.0033.0 2.653 2.656 0.0033.2 2.653 2.656 0.0033.4 2.653 2.656 0.0033.6 2.653 2.656 0.0033.8 2.653 2.656 0.0034.0 2.288 2.305 0.0174.2 2.288 2.305 0.0174.4 2.183 2.191 0.0084.6 1.969 1.981 0.0124.8 1.969 1.981 0.012

TABLE 5Performance Comparison Between the UPS Policy and theInterweave Paradigms for Different Primary Session Rate

Requirements

RateRequirements

UPS InterweaveParadigm

Rð1Þ; Rð2Þ Feasiblein PN

SSUtility

Feasiblein PN

SSUtility

Region 1

0 Yes 3.7012 Yes 3.04020.2 Yes 3.288 Yes 1.8990.4 Yes 3.288 Yes 1.8990.6 Yes 3.288 Yes 1.8990.8 Yes 3.288 Yes 1.8991.0 Yes 3.288 Yes 1.8991.2 Yes 3.288 Yes 1.2631.4 Yes 3.288 Yes 1.2631.6 Yes 3.288 Yes 1.2631.8 Yes 3.158 Yes 1.425

Region 2

2.0 Yes 3.158 Yes �12.2 Yes 3.158 Yes �12.4 Yes 3.158 Yes �12.6 Yes 2.892 Yes �12.8 Yes 2.653 Yes �13.0 Yes 2.653 Yes �13.2 Yes 2.653 Yes �13.4 Yes 2.653 Yes �13.6 Yes 2.653 Yes �13.8 Yes 2:653 Yes �1

Region 3

4.0 Yes 2.288 No N/A4.2 Yes 2.288 No N/A4.4 Yes 2.183 No N/A4.6 Yes 1.969 No N/A4.8 Yes 1.969 No N/A

Region 4

5.0 Yes �1 No N/A5.2 Yes �1 No N/A5.4 Yes �1 No N/A5.6 Yes �1 No N/A5.8 Yes �1 No N/A6.0 Yes �1 No N/A6.2 Yes �1 No N/A6.4 Yes �1 No N/A6.6 Yes �1 No N/A6.8 Yes �1 No N/A

Region 5 7.0 No N/A No N/A


Comparing columns four and six, we can find that the sec-ondary sessions always achieve higher utility objectivesunder the UPS policy than that under the interweave para-digm. This confirms our expectation that the UPS policy canoffer higher throughput for the secondary sessions.

As an example, consider the case when both the twoprimary sessions have rate requirements 1.6. The utilityobjectives achieved for the secondary sessions under theUPS policy and the interweave paradigms are 3.288 and1.263, respectively. Specifically, the rates for the two sec-ondary sessions are 4.784 and 5.692 under the UPS pol-icy while the rates for the same two secondary sessionsare 1.776 and 2.024 under the interweave paradigm.Under the UPS policy, the flow routing and schedulingfor the primary and secondary sessions are shown in

Fig. 4a. The number in the box on each link representsthe active time slots for this link. Note that primarynodes P7; P9 and P13 are helping relay secondarysessions’ data while secondary nodes S1; S3; S10 and S15

are helping relay the primary sessions’ data. In compari-son, under the interweave paradigm, the flow routingand scheduling for the primary network is shown inFig. 4b. According to the time slots used by the primarynetwork, the secondary network calculates the remainingtime slots at each node and uses them to maximize theirrate utilities. The flow routing and scheduling for thesecondary sessions under the interweave paradigm arealso shown in Fig. 4b. As expected, there is no coopera-tion at the node level between the two networks in termsof relaying each other’s data.

Region 2. This region represents the scenario where therate requirements of the primary sessions can be supportedunder both the UPS policy and the interweave paradigm,while the secondary sessions can only be supported underthe UPS policy but not under the interweave paradigm(with zero rate for some sessions and thus �1 rate utility).This region contains that the combined network can offermore to the secondary sessions than the isolated networksunder the interweave paradigm.

As an example, consider the case when the two pri-mary sessions have rate requirements 3.0. The utilityachieved for the secondary sessions under the UPS policyis 2.653. Specifically, the rates for the two secondary ses-sions are 3.753 and 2.793, respectively. Under the UPSpolicy, the flow routing and scheduling for the primaryand secondary sessions are shown in Fig. 5a. Note thatprimary nodes P7; P9; and P10 are helping relay secondarysessions’ data while secondary nodes S1; S3; S7; S10 andS15 are helping relay the primary sessions’ data. Underthe interweave paradigm, the flow routing and schedul-ing for primary network are shown in Fig. 5b. Based onthe time slots used by the primary network, the remain-ing time slots are not enough to support the secondarysessions, resulting in at least one of the secondary ses-sions with zero rate. Therefore, the rate utility for the sec-ondary sessions is �1 under the interweave paradigm.

Region 3. This region represents the scenario where therate requirements of the primary sessions can be supportedunder the UPS policy but not so under the interweave para-digm. For the secondary sessions, there is still remainingresource to support them under the UPS policy. For fairnessin comparison, we do not consider the rate utilities of the sec-ondary sessions under the interweave paradigm (marked as“N/A”). Region 3 shows the definitive advantage of using acombined network from the primary sessions’ perspectiveover the interweave paradigm.

As an example, we consider the case when the two pri-mary sessions have rate requirements 4.2. The utility objec-tives achieved by secondary sessions are 2.288 under theUPS policy. Specially, the rates for the two secondary ses-sions are 3.047 and 3.289, respectively. Under the UPS pol-icy, the flow routing and scheduling for primary andsecondary sessions are shown in Fig. 6. Note that primarynodes P7 and P14 are helping relay secondary sessions’ datawhile secondary nodes S3; S5; S10 and S15 are helping relaythe primary session’ data.

Fig. 5. Region 2 example that showing the flow routing topologies andscheduling for the primary and secondary sessions.


Region 4. This region represents the scenario where therate requirement of the primary sessions can be satisfiedunder the UPS policy but not so under the interweave para-digm. The secondary sessions can no longer be supportedunder the UPS policy (with zero rate for at least one sessionand thus �1 rate utility). For fairness in comparison, we donot consider the rate utilities of the secondary sessionsunder the interweave paradigm (marked as “N/A”) as eventhe rate requirements for the primary sessions cannot besupported. Similar to Region 3, this region shows the advan-tage of using a combined network to support the primarysessions over the interweave paradigm

Region 5. As the rate requirements of the primary ses-sions continue to increase, even the UPS policy will no lon-ger be able to support them after certain point. This isshown in Region 5.

6.3 Varying the Number of Nodes

In this section, we assume there are two primary sessions inthe primary network and two secondary sessions in the sec-ondary network. We fix the locations of source and destina-tion nodes of the primary and secondary sessions as shownin Fig. 7. Then, we increase the number of primary and sec-ondary nodes (K) in the network, and these nodes are uni-formly deployed in the 100 100 area. Since theseadditional primary and secondary nodes only serve as relaynodes under UPS, there are no distinction between the twotypes of nodes.

Table 6 shows the average SS utility objective (over 100network instances) under different number of nodes ðKÞ inthe primary and secondary networks for the case when

Rð1Þ ¼ 1:0 and Rð2Þ ¼ 1:0. When K ¼ 5 and K ¼ 10, thenetwork is not dense enough and is not entirely connected.Therefore, the SS utility objectives are both �1 (i.e., theachievable secondary sessions rate is 0 in both cases). WhenK ¼ 15; 20; 25; 30, the average SS utility objectives increasewith the number of usersK.

Then we vary Rð1Þ and Rð2Þ under different network sizeK. Fig. 8 shows the SS utility objectives under different net-

work size K when Rð1Þ and Rð2Þ vary. Again, for a given

rate for Rð1Þ and Rð2Þ, we have higher SS utility objectivesunder larger values ofK.

Fig. 6. Region 3 example that showing the flow routing topologies andscheduling for the primary and secondary sessions in the UPS policy.

Fig. 7. Locations of the source and destination nodes of the primary andsecondary sessions.

Fig. 8. Comparison of the SS utility objectives for different number ofnodes (K ¼ 10; 15; 20; 25; and 30) with the increasing rate requirementsfor the primary sessions.

TABLE 6Average SS Utility Objectives for

DifferentK Users

User NumberK SS utility objectives

5 �110 �115 1:929320 2:665325 3:223130 3:4772


6.4 Varying Session Numbers

In this section, we vary the primary and secondary sessionnumbers. We randomly generate a 20-node primary net-work and a 20-node secondary network as shown in Fig. 9.In the first part, we will keep the number of secondary ses-sions fixed and vary the number of primary sessions. In thesecond part, we will do the converse, i.e., keep the numberof primary sessions fixed and varying the number of sec-ondary sessions. In both parts, we will compare the perfor-mance under the UPS policy and the interweave paradigm.

Varying the number of primary sessions. Suppose thatthere are two secondary sessions, with each session’s sourceand destination nodes being ðS11; S7Þ and ðS4; S1Þ, respec-tively. By keeping these secondary sessions fixed, weincrease the number of primary sessions. The source anddestination nodes of each additional primary session is ran-domly chosen from the remaining primary nodes. Oncechosen, we assume it has a data rate requirement of 1.8 andis added on top of the existing primary sessions. Table 7shows our results. The first column in the table shows theincreasing number of the primary sessions. The second and

fourth columns show whether the additional new primarysession can be accommodated (feasible) under UPS andinterweave, respectively. Comparing these two columns,we can find that the maximum number of the primary ses-sions under UPS (7) is larger than that under interweave (5).The third and fifth columns show the utility function of thesecondary sessions under UPS and interweave. Comparingthese two columns, we can see that UPS achieves higherutility objectives than interweave. In summary, both pri-mary and secondary sessions benefit more from UPS thaninterweave.

Varying the number of secondary sessions. Now we dothe converse. Suppose there are two primary sessions, witheach session’s source and destination nodes being ðP9; P17Þand ðP1; P15Þ, respectively. The data rate requirement foreach primary session is 1.8. By keeping these primary ses-sions fixed, we increase the number of secondary sessions.The source and destination nodes of each additional sec-ondary session is randomly chosen from the remaining sec-ondary nodes. Once chosen, we add it on top of the existingsecondary sessions. Table 8 shows our results. The first col-umn in the table shows the increasing number of secondarysessions. The second and third columns show the utility val-ues of the secondary sessions under UPS and interweave,respectively. Comparing these two columns, we can findthat the maximum number of the secondary sessions thatcan be supported under UPS (8) is larger than that underinterweave (4). Further, for the same number of secondarysessions (from 1 to 8), the achieved utility value under UPSis higher than that under interweave.

7 CONCLUSIONS AND FURTHER WORK

In this paper, we develop a policy-based network coopera-tion paradigm as a new dimension for spectrum sharingbetween the primary and secondary users. Such networkcooperation can be defined as a set of policies under whichdifferent degrees of cooperation are to be achieved. The ben-efits of this paradigm are numerous, including improvednetwork connectivity and spatial diversity, increased flexi-bility in scheduling and routing, cost savings in infrastruc-ture needed for each individual network, among others. Forthe purpose of performance study, we consider a specificpolicy called UPS, which allows a complete cooperationbetween the primary and secondary networks at the nodelevel to relay each other’s traffic. We studied a problem

Fig. 9. A 20-node primary network and a 20-node secondary network.

TABLE 8Secondary Sessions’ Utility Values Under

Increasing Number of the Secondary Sessions

Number ofSecondary Session

UPS Interweave

1 2.228 1.3552 3.21 2.8523 4.594 2.6524 4.738 0.9435 4.253 �16 2.418 �17 2.307 �18 1.134 �19 �1 �1

TABLE 7Feasibility Performance of the Primary Sessions andUtilities of the Secondary Sessions Under Increasing

Number of the Primary Sessions

Number OfPrimary Session

UPS Interweave Paradigm

Feasiblein PN

SecondaryUtility

Feasiblein PN

SecondaryUtility

0 Yes 3.69 Yes 2.2191 Yes 3.446 Yes 1.6932 Yes 3.058 Yes 0.9313 Yes 2.661 Yes 0.8054 Yes 2.118 Yes �15 Yes 0.83 Yes �16 Yes �1 No N/A7 Yes �1 No N/A8 No N/A No N/A


with the goal of supporting the rate requirement of the pri-mary network traffic while maximizing the throughput ofthe secondary sessions. Through rigorous mathematicalmodeling, problem formulation, approximation solution,and simulation results, we showed that the UPS offers sig-nificantly better throughput performance than that underthe interweave paradigm.

In our future work, we will explore other policies underthe policy-based network cooperation paradigm. Under agiven policy, data forwarding behavior may also be affectedby user requirements and performance objectives. Suchuser requirements and performance objectives under a par-ticular policy are many, and each scenario would result indifferent data forwarding for both the primary and the sec-ondary sessions. Clearly, there is a large landscape for fur-ther research under this new paradigm. We hope our visionand results in this paper will open the door for furtherresearch in this area.

ACKNOWLEDGMENTS

This work was supported in part by US NSF grants 1343222,1064953, 1405747, 1443889, and ONR Grant N000141310080.The work of S. Kompella was supported in part by theONR. Part of W. Lou’s work was completed while she wasserving as a Program Director at the NSF. Any opinion,findings, and conclusions or recommendations expressed inthis paper are those of the authors and do not reflect theviews of the NSF.

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Xu Yuan (S’13-M’16) received the BS degree incomputer science from the Nankai University,Tianjin, China, in 2009. Since the Fall 2010, hehas been working toward the PhD degree in theBradley Department of Electrical and ComputerEngineering, Virginia Tech, Blacksburg, VA, USA.His current research interests include algorithmdesign and optimization for cognitive radio net-works. He is a member of the IEEE.


Yi Shi (S’02-M’08-SM’13) received the PhDdegree in computer engineering from the VirginiaTech, Blacksburg, VA, USA in 2007. He is currentlya senior research scientist at Intelligent Automa-tion, Inc., Rockville,MD,USA, andanadjunct assis-tant professor at Virginia Tech. His researchinterests include optimization and algorithm designfor wireless networks. He received the IEEE INFO-COM 2008 Best Paper Award and the only BestPaper Award Runner-Up of IEEE INFOCOM 2011.He is a senior member of the IEEE.

Xiaoqi Qin (S’13) received the BS and MSdegree in computer engineering from the VirginiaTech, Blacksburg, VA, USA, in 2011 and 2013,respectively. Since Fall 2013, she has been work-ing toward the PhD degree in the Bradley Depart-ment of Electrical and Computer Engineering,Virginia Tech. Her current research interestsinclude algorithm design and cross-layer optimi-zation for wireless networks. She is a studentmember of the IEEE.

Y. Thomas Hou (F’14) received the PhD degreefrom NYU Polytechnic School of Engineering (for-merly Polytechnic Univ.), New York, NY, USA. Heis currently the Bradley distinguished professor ofelectrical and computer engineering, VirginiaTech, Blacksburg, VA, USA. His current researchinterest include developing innovative solutions tocomplex cross-layer optimization problems inwireless and mobile networks. He has publishedtwo graduate textbooks: Applied OptimizationMethods for Wireless Networks (Cambridge Uni-

versity Press, 2014) and Cognitive Radio Communications and Net-works: Principles and Practices (Academic Press/Elsevier, 2009). He isthe steering committee chair of IEEE INFOCOM conference and a mem-ber of the IEEE Communications Society Board of Governors. He is afellow of the IEEE.

Wenjing Lou (F’15) received the PhD degree inelectrical and computer engineering from the Uni-versity of Florida, Gainesville, FL, USA. She iscurrently a professor in the Department of Com-puter Science, Virginia Tech, Blacksburg, VA,USA. Her research interests include the broadarea of wireless networks, with special emphaseson wireless security and cross-layer network opti-mization. Since August 2014, she has been serv-ing as a program director at the US NationalScience Foundation. She is the steering commit-

tee chair of the IEEE Conference on Communications and NetworkSecurity (CNS). She is a fellow of the IEEE.

Sastry Kompella (S’04-M’07-SM’12) receivedthe PhD degree in computer engineering fromthe Virginia Tech, Blacksburg, VA, USA, in 2006.He is currently the head of wireless network the-ory section, Information Technology Division,U.S. Naval Research Laboratory, Washington,DC, USA. His research interests include complexproblems in cross-layer optimization and schedul-ing in wireless and cognitive radio networks. He isa senior member of the IEEE.

Scott F. Midkiff (S’82-M’85-SM’92) is currently aprofessor and the vice president for informationtechnology and chief information officer at Vir-ginia Tech, Blacksburg, VA, USA. From 2009 to2012, he was the department head of the BradleyDepartment of Electrical and Computer Engineer-ing at Virginia Tech. From 2006 to 2009, heserved as a program director at the US NationalScience Foundation. His research interestsinclude wireless and ad hoc networks, networkservices for pervasive computing, and cyber-

physical systems. He is a senior member of the IEEE.

Jeffrey H. Reed (F’05) received the PhD degreefrom the University of California, Davis, CA, USAin 1987. He is the Willis G. Worcester professorin the Bradley Department of Electrical and Com-puter Engineering, Virginia Polytechnic and StateUniversity, Blacksburg, VA, USA. From June2000 to June 2002, he was the director of theMobile and Portable Radio Research Group. In2005, he founded Wireless at Virginia Tech andserved as its director until 2014. He is co-founderof Cognitive Radio Technologies, LLC, and Power

Fingerprinting, Inc. His area of expertise is in software radios, cognitiveradio, wireless networks, and communications signal processing. He is adistinguished lecturer for the IEEE Vehicular Technology Society. He is afellow of the IEEE.

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